arXiv 1306.10222013-06gr-qchep-thmath-phmath.COmath.MP

Ben Geloun-Rivasseau张量场论的组合Hopf代数

Combinatorial Hopf algebra for the Ben Geloun-Rivasseau tensor field theory

Matti Raasakka, Adrian Tanasa

备注：: accepted for publication in Seminaire Lotharingien de Combinatoire; 32 pages (plus 6 scrap pages due to arXiv compiler), 17 figures, 2 tables; reduced review on Hopf algebra basics and several minor clarifying modifications w/r to the previous version
发表信息：: Seminaire Lotharingien de Combinatoire 70 (2014), B70d

摘要：

本·吉隆-里瓦索量子场论模型是第一个被证明是微扰重整化的张量模型。我们在这里定义一个适当的Hopf代数描述这个新的张量重整化的组合。我们提出的结构是显着不同，从以前定义的Connes-Kreimer组合Hopf代数由于所涉及的张量Feynman图的组合和拓扑性质。特别是，2-和4-点函数插入必须被定义为非平凡的，只有当相关的费曼积分的表面发散度是保守的。

英文摘要：

The Ben Geloun-Rivasseau quantum field theoretical model is the first tensor model shown to be perturbatively renormalizable. We define here an appropriate Hopf algebra describing the combinatorics of this new tensorial renormalization. The structure we propose is significantly different from the previously defined Connes-Kreimer combinatorial Hopf algebras due to the involved combinatorial and topological properties of the tensorial Feynman graphs. In particular, the 2- and 4-point function insertions must be defined to be non-trivial only if the superficial divergence degree of the associated Feynman integral is conserved.

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